A method for incorporating variable costs and differing precision requirements into optimal design theory is developed and discussed. In many studies and experiments, particularly in the biological sciences, the cost of each observation can vary considerably depending on the attributes of the sample. Ignoring observation costs leads to designs that maximize precision for a given sample size. However, by incorporating costs, efficiency is maximized by optimizing precision per unit cost. An example is presented that demonstrates the efficiency of a weighted optimal design in comparison with several alternatives. The weighted optimal design is most efficient at meeting the experimenter's precision objectives. Comparing designs allows the introduction of additional criteria such as design flexibility into the evaluation process. Explicitly incorporating both cost and precision in the search for a sampling design ensures time is wisely spent considering study objectives, including precision requirements.
A Convergence Theorem in $L$-Optimal Design Theory
